The calorimeter jet energy scale can be probed by comparing the measured jet energy to that of a well-calibrated reference object with independent systematic uncertainties. Charged-par-ticle tracks are well measured with uncertainties independent of the calorimeter, and can be associated with jets, are used here.
The mean value of rtrk, defined in Eq. (19) is primarily sensi-tive to the particle composition of the jet and thus should be well described by any well-tuned event generator. In comput-ing hrtrki it is important to truncate the rtrk distribution (here with rtrk< 3) to avoid contributions from fake tracks with un-physically large pT.
To verify the description of the calorimeter energy mea-surement in MC simulations, the double ratio of the
charged-to-total momentum obtained in data to that obtained in Monte Carlo simulation is studied:
Rrtrk≡hrtrkiData
hrtrkiMC. (20)
The ratio is evaluated for inclusive jets (Rrtrk,inclusive), b-tagged jets (Rrtrk,b-jet) and b-tagged jets with a reconstructed muon in-side (Rµ νr
trk,b-jet, in the dijet sample only). The calorimeter re-sponse ratio R0of b-tagged jets relative to inclusive jets is then defined using Eq. (20) from each respective sample,
R0≡ Rrtrk,b-jet
Rrtrk,inclusive. (21) This ratio is used to test the relative systematic uncertainty be-tween b-tagged and inclusive jets. In the t ¯t sample, where the fraction of b-jets is large (≈ 50%), the light jets (non b-tagged) component is used in the denominator instead of the inclusive one. It is mainly comprised of jets from the W boson decay but also to a lesser extent of gluon jets from initial- and final-state radiation. As a consequence, when comparing the results ob-tained in the t ¯t and the dijet analyses, the difference in terms of jet flavour components entering the calculation of Rrtrk,inclusive needs to be taken into consideration.
19.6 Systematic uncertainties
Systematic uncertainties in the rtrkmeasurement arise from the modelling of the jet (and b-jet) fragmentation, b-tagging cal-ibration, jet resolution and track reconstruction efficiency. In
[GeV]
T
pjet
40 102 2×102 103 2×103
MC incl>trk/<rData incl>trk=<rrtrk inclR
0.85
MC incl>trk/<rData incl>trk=<rrtrk inclR
0.85
Relative Syst Uncertainty for inclusive jets
0 Tracking in Jet Core
|<1.2
MCb-jets>trk/<r Datab-jets>trk=<rrtrk b-jetR
0.85
2011 data / Pythia MC11
Total syst -1
Relative Syst Uncertainty for b-jets
0
MCincl>trk/<rDataincl>trk<r
MCb-jets>trk/<r Datab-jets>trk<r R’=
0.85
2011 data / Pythia MC11
Total syst -1
trkinclusive / r trk b-jets Relative Syst Uncertainty for r
0
Fig. 54: Ratio of the average rtrkgiven in Eq. (19) in data and MC simulations for(a)inclusive jets and(c)tagged b-jets. In(e), the b-tagged to inclusive sample ratio variable R0from Eq. (21) is shown. The contributions of the systematic uncertainties to the total uncertainty in the different measurements are shown in(b),(d), and(f), respectively. Jets within |η| < 1.2 are used.
[GeV]
jet
pT
20 30 40 50 60 102 2×102 3×102
MClight>trk/<rDatalight>trk=<rrtrk lightR
0.85
l+jets / Pythia MC11 t
MCb-jets>trk/<rDatab-jets>trk=<rrtrk b-jetR
0.85
l+jets / Pythia MC11 t
MClight>trk/<r Datalight>trk<r
MCb-jets>trk/<r Datab-jets>trk<r R’=
0.85
l+jets / Pythia MC11 t
Fig. 55: Ratio of the average rtrkgiven in Eq. (19) in t ¯t events in data and MC simulations for(a)light-jets and tagged(c)b-jets.
In (e), the ratio of Rrtrk from Eq. (20) between the b-jet and the light-jet sample is shown. The total systematic uncertainty is shown as a band, and the dotted lines correspond to unity and the 2.5% deviation from unity. The contributions of the systematic uncertainties to the total uncertainty in the different measurements are shown in(b),(d), and(f), respectively. The contributions to the total systematic uncertainty due to the jet resolution, b-tagging calibration, background contamination and the modelling of the initial- and final-state radiation are grouped under “Other systematics”. Jets with |η| < 1.2 are used.
[GeV]
truth
pT
50 100 150 200 250
Response All Particles
0.85 0.9 0.95 1 1.05
1.1
PYTHIA MC11 Inclusive jets b-jet MV1@70%
ν) µ
→ b-jet(b
|<0.8 η
| R=0.4
anti-kt
=7 TeV s
ATLAS Simulation
(a)
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jet
pT
20 40 60 80 100 120 140 160 180 200
Correction
0.95 1 1.05
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= 7 TeV s PYTHIA MC11,
R=0.4 anti-kt
Central value Tagging Syst.
Decay Spectrum Syst.
Others
Combined Systematic
|<0.8 η
=4 GeV, |
µ
pT
[GeV]
jet
pT
20 40 60 80 100 120 140 160 180 200 ATLAS Simulation
Uncertainty 0
0.02 0.04
(b)
Fig. 56: Average jet response as a function of true transverse momentum of jets built using all stable particles, for a sample of inclusive jets (solid circles), a sample of b-jets tagged with the MV1 tagging algorithm (open circles) and a sample of semilep-tonically decaying b-jets with a reconstructed muon inside (open squares), is shown in(a). The resulting semileptonic correction, as a function of calorimeter jet pT, used to transform the pTof a jet in the semileptonic sample to the pTof a jet in an inclusive sample of b-jets, is displayed in(b). Associated systematic uncertainties are shown around the central value, and the combined uncertainty is shown as a coloured band.
addition, for high-pTjets (pT> 500 GeV) an efficiency loss in the tracking in the jet core is observed in MC simulations, and a systematic uncertainty is added to account for potential mis-modelling of this effect. These uncertainties are assumed to be uncorrelated. The resulting fractional systematic uncertainties on rtrkand R0are shown in Figs.54(b),54(d), and54(f)for the inclusive jet sample, and in Figs.55(b),55(d), and55(f)for the t ¯tsample. They are determined as follows.
1 MC generator and tunes
These systematic uncertainties capture the effects of dif-ferences in ptrkT caused by different fragmentation models.
Differences in the calorimeter response, caused by the dif-ferent particle spectra, can also impact the rtrkmeasurement in certain MC simulations and should not be part of the un-certainty, since such shifts are measurable in the data. The rtrk distribution is, thus, calculated from the various sam-ples described in Sect.3 using ptruthT in the denominator, even though only small differences are observed when in-cluding calorimeter effects, i.e. using pcaloT in most samples.
In the top pair analysis, differences between MC@NLO and POWHEG+HERWIGare considered as process or gen-erator systematic uncertainties. Fragmentation and decay systematic uncertainties are evaluated taking the difference between PYTHIA and HERWIG. In the dijet analysis, dif-ferences between PYTHIAand HERWIG++ set the system-atic uncertainties from uncertainties in the decay models.
The updated fragmentation tune in HERWIG++ prevents this comparison from being a conservative measure of the
b-jet fragmentation systematic uncertainties. These are eval-uated using comparisons to the Bowler–Lund and Professor tunes described before.
2 b-tagging calibration
The scale factors that correct the b-tagging efficiencies in MC simulations to match the measured values are varied within their total uncertainty.
3 Material description
The knowledge of the tracking efficiency modelling in MC simulations is evaluated in detail in Ref. [97]. The system-atic uncertainty on the tracking efficiency for isolated tracks increases from 2% (|ηtrack| < 1.3) to 7% (2.3 ≤ |ηtrack| <
2.5) for tracks with pT> 500 MeV. The resulting effect on rtrk is about 3% for 0 ≤ |η | < 2.1 and about 4% for 2.1 ≤ |η | < 2.5.
4 Tracking in jet core
High track densities in the jet core influence the tracking ef-ficiency due to shared hits between tracks, fake tracks and lost tracks. The number of shared hits is well described in the MC simulation. The pTcarried by fake tracks is negligi-ble. A relative systematic uncertainty of 50% on the loss of efficiency obtained in the simulation is assigned to account for potential mis-modelling of this effect.
5 Jet energy resolution
The jet energy resolution in MC simulations is degraded by about 10%.
6 Background contamination
For the t ¯t sample the analysis is repeated including the
ex-pected background contamination (except the multijet con-tribution) and the full difference is taken as an estimate of the systematic uncertainty.
The dominant contributions to the systematic uncertainty in the t ¯t analysis are due to variations in the detector material and fragmentation/decay models. In the dijet sample, the ma-terial, fragmentation and decay uncertainties also dominate the systematic uncertainties, except at pT& 500 GeV where the uncertainty caused by the loss of efficiency in the jet core dom-inates. In Fig.55, the contributions to the total systematic un-certainty due to the jet resolution, b-tagging calibration, back-ground contamination and due to the modelling of the initial-and final-state radiation are labelled as “other” systematic un-certainties.
For R0, the tracking components (the material description, impacting the tracking efficiency) of the systematic uncertainty entering both the numerator and denominator are correlated and thus approximately cancel. A similar consideration holds for the jet energy resolution. The most significant systematic